Kerala Syllabus Class 8 Mathematics - Unit 1 Squares - Questions and Answers | Teaching Manual 

Questions and Answers for Class 8 Mathematics - Unit 1 Squares - Study Notes | Text Books Solution STD 8 - Maths: Unit 1 Squares - Questions and Answers | ഗണിതം - വർഗങ്ങൾ - ചോദ്യോത്തരങ്ങൾ 

എട്ടാം ക്ലാസ്സ്‌  Mathematics - Unit 1 Squares എന്ന പാഠം ആസ്പദമാക്കി തയ്യാറാക്കിയ ചോദ്യോത്തരങ്ങള്‍. ഈ അധ്യായത്തിന്റെ Teachers Handbook, Teaching Manual എന്നിവ ഡൗൺലോഡ് ചെയ്യാനുള്ള ലിങ്ക് ചോദ്യോത്തരങ്ങളുടെ അവസാനം നൽകിയിട്ടുണ്ട്. പുതിയ അപ്‌ഡേറ്റുകൾക്കായി ഞങ്ങളുടെ Telegram Channel ൽ ജോയിൻ ചെയ്യുക.

Kerala Syllabus STD 8 Maths: Unit 1 Squares - Textbook Solutions

♦ Textbook Activities (Textbook Page No: 11)
Perfect squares

♦ Calculate the squares given below. 
(i) 64², (ii) 35², (iii) 47², (iv) 53², (v) 88²
Answer:
(i) 64²
64² = 60² + (60 × 4 × 2) = 4²
      = 3600 + 480 + 16
      = 4096

(ii) 35²
35² = 30² + (30 × 5 × 2) = 5²
      = 900 + 300 + 25
      = 1225

(iii) 47²
47² = 40² + (40 × 7 × 2) = 7²
      = 1600 + 560 + 49
      = 2209

(iv) 53² 
53² = 50² + (50 × 3 × 2) = 3²
      = 2500 + 300 + 9
      = 2809

(v) 88²
88² = 80² + (80 × 8 × 2) = 8²
      = 6400 + 1280 + 64
      = 7744

♦ Textbook Activities (Textbook Page No: 13)
Decimal squares

♦ Find the squares of the numbers below:
(i) 2.3, (ii) 8.7, (iii) 10.1, (iv) 12.5, (v) 15.7
Answer:
(i) 2.3
2.3² = 2² + (2 × 0.3 × 2) + (0.3)²
      = 4 + 1.2 + 0.09
      = 5.29

(ii) 8.7
8.7² = 8² + (8 × 0.7 × 2) + (0.7)²
      = 64 + 11.2 + 0.49
      = 75.69

(iii) 10.1
10.1² = 10² + (10 × 0.1 × 2) + (0.1)²
         = 100 + 2 + 0.01
         = 102.01

(iv) 12.5
12.5² = 12² + (12 × 0.5 × 2) + (0.5)²
         = 144 + 12 + 0.25
         = 156.25

(v) 15.7
15.7² = 15² + (15 × 0.7 × 2) + (0.7)²
         = 225 + 21 + 0.49
         = 246.49

♦ Textbook Activities (Textbook Page No: 14)

♦ Look at these computations:
Can you calculate 4.5² like this?
Take some more numbers with decimal part 0.5 and calculate their squares. Can you find a simple method to calculate the squares of such numbers?
4.5² = 4² + (4 × 0.5 × 2) + (0.5)²
       = 16 + 4 + 0.25
       = 20.25
5.5² = 5² + (5 × 0.5 × 2) + (0.5)²
       = 25 + 5 + 0.25
       = 30.25
7.5² = 7² + (7 × 0.5 × 2) + (0.5)²
       = 49 + 7 + 0.25
       = 56.25
8.5² = 8² + (8 × 0.5 × 2) + (0.5)²
       = 64 + 8 + 0.25
       = 72.25
From the above examples, we can arrive at a general conclusion.
All numbers whose decimal part is 0.5 are of the form n + 0.5.
∴ (n + 0.5²) = n² + (n × 0.5 × 2) + (0.5)²
                  = n² + 1n + 0.25
                  = n² + n + 0.25
                  = n(n + 1) + 0.25
Using this, we can easily find out the following squares.
1.5² = 1 (1 + 1) + 0.25 = 0.25 = 2.25
2.5² = 2 x 3 + 0.25
       = 6 + 0.25 = 6.25
3.5² = 3 x 4 + 0.25
       = 12 + 0.25 = 12.25
4.5² = 4 x 5 + 0.25 = 20.25
5.5² = 5 x 6 + 0.25 = 30.25
6.5² = 6 x 7 + 0.25 = 42.25
7.5² = 7 x 8 + 0.25 = 56.25
8.5² = 8 x 9 + 0.25 = 72.25
9.5² = 9 x 10 + 0.25 = 90.25
10.5² = 10 x 11 + 0.25 = 110.25

(2) Look at these computations:
1.25² = 1² + (2 × 1 × 0.25) + (0.25)² = 1 + 0.5 + 0.0625 = 1.5625
2.25² = 2² + (2 × 2 × 0.25) + (0.25)² = 4 + 1 + 0.0625 = 5.0625
3.25² = 3² + (2 × 3 × 0.25) + (0.25)² = 9 +1.5 + 0.0625 = 10.5625
4.25² = 4² + (2 × 4 × 0.25) + (0.25)² = 16 + 2 + 0.0625 = 18.0625
Take some more numbers with decimal part 0.25 and calculate their squares. Is there a general method to compute such squares?
5.25² = 5² + (5 × 0.25 × 2) + (0.25)²
         = 25 + 2.5 + 0.0625
         = 27.5625
6.25² = 6² + (6 × 0.25 × 2) + (0.25)²
         = 36 + 3 + 0.0625
         = 39.0625
7.25² = 7² + (7 × 0.25 × 2) + (0.25)²
         = 49 + 3.5 + 0.0625
         = 52.5625
8.25² = 8² + (8 × 0.25 × 2) + (0.25)²
         = 64 + 3.5 + 0.0625
         = 68.0625
From the above examples, we can arrive at a general conclusion.
All numbers whose decimal part is 0.25 are of the form n + 0.25.
∴ (n + 0.25²) = n² + (n × 0.25 × 2) + (0.25)²
                  = n² + 0.5n + 0.0625
                  = n (n + 0.5) + 0.0625
Using this, we can easily find out the following squares.
1.25² = 1 × 1.5 + 0.0625 = 1.5625
2.25² = 2 × 2.5 + 0.0625 = 5.0625
3.25² = 3 × 3.5 + 0.0625 = 10.5625
4.25² = 4 × 4.5 + 0.0625 = 18.0625
All such numbers with decimal 0.75 are in the form n + 0.75.
∴ (n + 0.75²) = n² + (n × 0.75 × 2) + (0.75)²
                  = n² + 1.5n + 0.5625
                  = n (n + 1.5) + 0.5625
Using this, we can easily find out the following squares.